was any solvent nor continuum included. The band shape of the lines was modelled, using the Gaussian standard broadening procedure, in the far-from-resonance approximation at room temperature.
Figure 2. The AMP molecule - fixed in one of the minimum S-ZH, S-ZC or S-ZN conformations, respectively, has a rotational degree of freedom around the C8-N bond. Depending on preselected values of the dihedral angle C7-C8-N-H (abscissa), the molecule minimum energy varies considerably, as can be seen from plots (a, b and c). The amplitude variation is large when the amino group has contact with the aromatic ring (a and b) and smaller when the amino has no contact (c). For the ion AMPH+—because of the 3-fold repetition symmetry of the NH3+ group around the C8-N bond—the situation is more simple: The minimum energy corresponds to the situation in which two ammonium protons approach the ring in the S-ZC conformation, see plot (d). All energy points shown correspond to conformations in the gas phase, totally minimized except for the fixing of the abscissa to the shown values.
3. Results and Discussion
The quantum chemical calculation results are reported in Tables 1-2 and in the figures. The optimized structures and the corresponding minimized energies of AMP and AMPH+ are given in Table 1 and Figure 1. Comparing the energy values, the S-ZC conformations of both AMP and AMP-H+ clearly represent the most stable conformation, see Figure 1.
Table 1. Minimum energies and dipole moments of the optimized structures of AMP and AMPH+, calculated by use of 6-311G+(d,p)/B3LYP/DFT modelling. The corresponding calculated ROA spectra of the S-species can be seen in Figure 5.
Table 2. Calculated vibrations of the AMPH+ ion in the S-ZN conformation according to gas phase 6-311G+(d,p)/B3LYP/ DFT modelling. Assignments are given for the modes that are also compared to measured Raman spectra of solid di-DAMPH+ sulfate [(D-AMPH)2SO4]. The columns are giving mode number, wavenumber, Raman intensity, ROA intensity, assignment of the mode and tentative assignment of the measured Raman spectrum (wavenumber, band intensity, respectively).
When studying the geometry of different AMP conformers, it was found that rotation of the NH2 amino group around the C8-N bond had an appreciable influence on the minimum energy. We investigated this influence by fixing the AMP molecule in each of the minimum S-ZH, S-ZC or S-ZN conformations, respectively, and minimizing the energy under the constraint that the dihedral C7-C8-N-H angles should stay at preselected values. These results were obtained with the Spartan program  using the same basis sets, and giving identical results. The dependence of the molecule minimum energy versus the dihedral angle (abscissa) is shown in Figure 2, plots (a, b and c). A considerable (amplitude) variation can be seen. The energy is low when a proton of the amino group has a near contact with the aromatic ring (plots a and b) and smaller when the amino has no contact (c).
The AMPH+ ion was found to behave somewhat differently, due to the 3-fold repetition symmetry of the ammonium NH3+ group around the C8-N bond. The situation is simpler: The minimum energy, see Figure 2, plot (d) corresponds to the situation in which two ammonium protons in the S-ZC conformation approach the aromatic ring.
We can compare this AMP calculation result to the results of Godfrey et al. . These authors also found ZC as the most stable conformer in the gas phase: Their “structure I” with the dihedral angle of 174˚ was given as the most stable geometry both experimentally (millimetrewave rotational spectroscopy) and by means of their MP2/6-31G(d,p) modelling. This result compares well with our molecule, see Figure 2(b). From their spectroscopic experiments Godfrey et al.  also—as is to be expected—found small amounts of another comformation (named “structure II”) with the dihedral angle of –54 (energy 1.4 kJ/mol). This agrees also well with our Figure 2(b). The explanation for the high stability of the ZC conformation seems to be due to the internal close contact between the aromatic electrons and one of the amino protons. This non-classical hydrogen bonding  feature is displayed in Figure 3 (the distance between C1 and H was around 2.675 Å).
For the AMPH+ ion in the gas phase, the agreement between model calculations and the experimental X-ray crystal structures is less obvious. We explain this in the following way: When the ion structure was optimized as a separate ion in the gas phase, the stabilization came from the close contact (around 2.675 Å) between C1 and one of the ammonium protons, see Figure 3. In the known crystal structures [36-38] the anions interfere with the AMPH+ cations, making the ZN conformation favorable. The stabilization energy must come from the crystal lattice.
3.2. ROA Spectroscopy
In ROA spectroscopy, or generally in vibrational optical
Figure 3. Comparison between the minimum calculated distance between the C1 and the amino H in the gas phase AMP molecule and the AMPH+ion. The reason for the stabilisation of these conformations seem to be the internal close contact between the aromatic electrons and the protons. In the known crystal structures the anions interfere and make S-ZN AMPH+ favorable.
activity spectroscopy, the large number of probed vibrational transitions makes it unlikely that a change in conformation of a chiral molecule should result in oppositely signed bands in the entire ROA spectrum . Therefore, it should be possible to achieve knowledge on the absolute configuration from associating measurements of the enantiomers with quantum chemical calculations.
When the ROA spectra were calculated by the Gaussian program for both AMP and AMPH+ species the output came out in several ways, one of them given as the invariant ICPu/SCPu (180˚) in units of 104 Å5/AMU (AMU = atomic mass units). As mentioned in section 1, for ROA experiments there are three possible polarization schemes of measurement and calculation. These schemes are referred to as ICP, SCP or DCP, respecttively), depending on the experiment. Since we used the SCPu setup and a collecting angle of 180˚, where “u” denotes unpolarized scattering, the invariant ICPu/SCPu (180˚) is the relevant one here.
As a check of the absolute configurations, we calculated the minimized energies of the two opposite enantiomers, R(–) and S(+), for example of the AMP ZN configuration. The results are included in Table 1. The optimized model of the S-ZN is the one shown in Figure 1; R-ZN looked exactly like the mirror image. The calculated corresponding ROA spectra of these AMP R-ZN and S-ZN conformers are given in Figure 4. As the theory predicts the spectra were completely opposite to each other, throughhout the whole wavenumber range (0 - 3500 cm–1), Also, to our satisfaction, the minimum energy and dipole moment were observed with identical values (Table 1).
Figure 4. Quantum Chemical DFT/B3LYP/6-311G+(d,p) calculated ROA spectra for the S-ZN (red) and the R-ZN AMP molecule conformer in the gas phase (magenta). The region where no significant vibration is noticed has been omitted.
Calculated ROA spectra of the three different AMP and three different AMPH+ species are compared in Figure 5. The spectra of all conformers of AMPH+ and AMP differ considerably from each other in the whole wave-number range. Protonation of the amino-group has a large influence on the ROA spectra (compare the spectra of the same color). This is quite similar to the behaviour found for the Raman spectra . Interestingly also the ROA spectra of AMP or AMPH+ respectively, depend on the internal rotation around the C7-C8 bond. This can only be interpreted as a result of the conformational isomerism, as depicted in Figure 1. It means that, even within the same species i.e. AMP or AMPH+, spectral differences arise as a result of different coupling schemes among the group vibrations depending on the geometry. Such a behavior has been seen before . This reveals that such differences are exclusively attributable to the internal rotations, as any chirality difference within the same species would have appeared in opposition to each other, as seen in Figure 4.
To compare these theoretical results with experiments we note that most available samples are amphetamine salts. A measured Raman spectrum of the solid di-D-AMPH+
Figure 5. Calculated ROA spectra for three different conformations of AMPH+ (above) and AMP (below) using quantum chemical DFT/B3LYP calculations. Gaussian 6-311G+(d,p) and 6-311G(d,p) split valence basis sets were used for AMP and AMPH+, respectively. The differences due to internal rotation are obvious when comparing the spectra. The region where no significant vibration is noticed has been omitted.
sulfate is shown in Figure 6. The correspondence between this experimental Raman spectrum and a Raman spectrum calculated with a DFT/B3LYP/6-311G(d,p) model has been discussed previously . In the present study the Raman and the ROA spectra for the AMPH+ ion were calculated with a better model. Some of the results (for the S-ZN AMPH+ ion) are reproduced in Table 2. The calculated ROA data can be seen in column 4 together with experimental data in the last column. Assignments for all 66 vibrations of the AMPH+ ion in the S-ZN conformation are given in the 5th column of Table 2, based on animated modes given by the Gaussian software . These 66 modes are compared to the experimental data—in the last column—see also Figure 6. The assigning of these observed bands to the calculated modes has been done based on best wavenumber matching and also on the strengths of the peaks. Differences are noticed between the measured and the calculated wavenumber values of the modes. This is to be expected and is probably due to the insufficient modelling of the solid salt by an ion gas phase model, even though the calculated conformation has the same specific internal rotation (S-ZN) as found in the salt [36,37]. Differences may also be due to the sulfate (hydrogen bonded to the ammonium group) and the presence of fluorescing impurities.
To compare the calculated ROA results with experiments, we measured ROA spectra of amphetamine-H+ sulfate standards purchased from Sigma-Aldrich and of two street “amphetamine” samples, Drug A and Drug B, dissolved in water. ROA spectra of Drug A and Drug B, depicted in red and blue, respectively, are compared in Figure 7. Unfortunately the signals were relatively weak compared to the noise. Remarkably however, these two samples seem to be different enantiomers of the same species, as seen most noticeably in the regions 1100-950 and 1650 - 1450 cm–1. The spectral bands in these “finger-print” regions are mainly due to N-H angle deformation, ring C-C stretching and C-H in ring plane angle deformations, according to our calculations (see Table 2). The region around 1000 cm–1 is highly characteristic for AMPH+, as it has been discussed before .
With regard to ROA spectra of the standard samples, the DL-AMPH+ sulfate solution, as expected, did not show any ROA activity: Equal amounts of the R and S conformations cancel the ROA signal. In contrast to this the di-D-AMPH+ sulfate standard solution gave an ROA spectrum that is shown in Figure 8, compared to the two street samples, Drugs A and B. Previously Raman spectra for the same samples were studied  and bands observed at 1006 cm–1 and 981 cm–1 have been assigned to the AMPH+ and ions, respectively (see also Table 2). It is worth mentioning that in spite of the fact that the ion has no direct chirality, its 981 cm–1 band can still be seen in the ROA spectrum. This is attributed to an
Figure 6. Raman spectrum of solid di-D-AMPH+ sulfate, obtained on a LABRAM instrument with 514.5 nm laser light excitation . The region where no significant vibration is noticed has been omitted.
Figure 7. ROA spectra of street samples dissolved in water: Drug A (blue) and Drug B (red). It seems from these spectra, as indicated with asterisks, that many peaks occur with opposite sign, shape and intensity, signalling opposite chirality. This is obvious especially in the 1050-950 cm–1 region. Some regions have been omitted.
interionic effect. It is known that interionic interactions may introduce chirality into non-chiral molecules or ions bound to chiral species. Here, the sulfate ions must certainly be interacting with the chiral AMPH+ ions by virtue of hydrogen bonds in the solution, somewhat similar to what was seen in the solid state [37,38]. The appearance of the signal in both of the spectra of Drugs A and B indicates that it is not likely to be an artefact.
When comparing the spectra in Figure 8, strong similarities between the standard sample and one of the street
Figure 8. ROA spectra of street sample solutions (in water) of Drug A and Drug B, compared to a solution of a purchased standard di-D-AMPH+ sulfate sample. The peaks marked with asterisks show quite a resemblance between the standard sample (black) and one of the street samples, Drug B (red), especially in the 1100-800 cm–1 region. The three ordinate scale magnitudes can be judged by compareson to Figure 7. For clarity some regions have been omitted.
samples (Drug B) can be noted (peaks marked with asterisks). This feature is most apparent in the lower wavenumber region (1100 - 800 cm–1). Unfortunately the noise level was too high to give details, suggesting that more studies deserve to be carried out on stronger concentrations.
The measured ROA spectrum of the di-D-AMPH+ sulfate is compared to the calculated results in Figure 9 (see also Figure 5). It appears to be most satisfactorily
Figure 9. Calculated ROA spectra of AMPH+ ions in different conformations, compared to a solution of standard di-D-AMPH+ sulfate. The peaks marked with asterisks are the ones that resemble peaks in the street sample, Drug B.
modelled by the calculated S-ZN AMPH+ spectrum, especially when taking notice more to the shapes than to exact matching of the wavenumbers. This is not surpriseing as the S-ZN form from the crystal may still be stabilised in solution via formation of hydrogen bonds, etc. The similarity between the experimental di-D-AMPH+ sulfate results and the AMPH+ S-ZN modelling has also been found for the Raman and SERS spectra .
The ROA spectra of chiral molecules can provide information about the absolute configuration, when one or both enantiomers are available. In this study we have obtained Raman and ROA spectra of different species of amphetamine (amphetamine and amphetamine-H+), in which internal rotations and chirality were included. Spectra of street drug samples have been compared to standard samples, showing them to possibly be different enantiomers of the same compound even though they give almost identical Raman spectra . Also the standard sample solution is likely to contain the AMPH+ ion in the S-ZN conformation, interacting with the sulfate ions.
Quantum Chemical DFT model calculations (geometry minimizations followed by calculation of Raman optical activity spectra) indicate that obtained preliminary ROA spectra can be used to assign the S(+)-amphetamine molecule and the S(+)-amphetamine-H+ ion to their different conformational states; the difference between these states being their internal rotation, i.e. the arrangements of the atoms or groups (H, CH3 or NH2/NH3+) bound to the C8 atom. This is the first time that ROA spectra of amphetamine compounds have been given. The spectra were used to characterize two street drug samples as being most likely opposite enantiomers of the same compound: Amphetamine-H+ sulfate. This compound (purchased and used as a standard solution) was found to adopt the S-ZN conformation in aqueous solution with C8 adopting the S-chirality and with the NH3+ group completing the letter Z in our notation for the different conformations.
Dr. Thomas Nørbygaard is thanked for help and advice during the ROA measurements. Director Ib Henriksen’s Foundation is thanked for maintenance of the Raman instrumentation. The Danish Fundamental Research Foundation as well as the Danish Agency for Science, Technology and Innovation (#09-065038/FTP) helped contribute funding for this project.